Capacitor's are no longer germane to jump technology in the MGT universe. Original Traveller had the hydrogen fuel being rapidly consumed to produce energy to power lanthanum jump grids from the capacitors. MGT has the hydrogen being used to create exotic hydrogen particles.

This is actually a good question to ask. The game doesn't really address it much, if at all. But I would say that there are always going to be some advances.

For example, consider the airliner toilet. What has changed since the days of the 727? For one thing, they're less likely to leak, dropping tainted ice bombs on houses under flight paths. For another, the toilet seat lid on newer airliners drops slowly and closes silently, minimizing the annoying racket (and occasional freak-outs from nervous fliers who don't recognize the source) of a hard dropping lid to people near the toilets. It's a small thing, but it's an advance -- and that airline technology spread to the home market, so now I have a silent toilet lid in one of my bathrooms.

For example, we've got copper pipes today in TL7 ships, but the technology for pipes hasn't changed much since their invention.

One change is manufacturing technology. I don't know how the Roman Empire built its lead plumbing, but my guess is that they were cast in tubes with rods down the middle. A lot of modern plumbing is made by extrusion, but installed by people. The plumbing in a Traveller starship might still be manufactured by extrusion, but installed by robots. Roman plumbing could probably be repaired by low-temperature welding, since lead has such a low melting point, or maybe the cold water pipes were fitted tightly with fats or oils to seal it. A lot of today's plumbing can be repaired only by replacing long sections between modular joints and discarding the good parts of the segments along with the bad. But maybe far future plumbing is some techno-magical substance that can be repaired by cutting out the broken ends, slipping in a guide rod and tube, squeezing instant pipe replacement goo in between, and then rinsing away the guide rod and tube with water -- but only if you have a supply of techno-magical plumbing goo and rinse-away guide rod and tube substance.

So would your TL12 life support system be radically (or any?) different than a TL15 one?

Per the rules, it doesn't seem so.

But the cost is different, if you go by economic model rules. If I remember correctly, TL12 products made with TL13 manufacturing cost half as much, with TL14 manufacturing they cost one-fourth as much, and with TL15 manufacturing there's no further cost reduction beyond that granted by two TLs of advance. But the advantage of using more advanced manufacturing are limited by exchange rates, which make each TL of advance 1.5 times more expensive, except for TL15 which is twice as much as TL14 because TL15 is the only source for TL15 goods, which reduces manufacturing capacity available for more efficient production of lower technology goods.

. . .
I would posit that TL12 life support tech is not really that much different than TL11 or TL15. Notice how the rules assume a TL9 stateroom supports the same number of people as a TL15 one does. SOME systems (power generation, M-drives, weapons, sensors) would benefit from increased TL. And maybe even the internal anti-grav systems would be able to handle additional Gs as the TL increases.

And at least in military ships and high acceleration express shuttles, lighters, tankers, etc. the G limit is a material benefit in something that definitely falls into the category of life support.

I think that the reason the rules don't grant advantage for technology advances in life support isn't that no one ever thought that it might be possible for a TL15 Murphy bed and bedclothes that squash up to the ceiling of a stateroom with only a centimeter of thickness, but are still as comfortable as a solid bed with a goose down blanket. It's just that no one thought that it was worth the added rules complication to make such a distinction, even if actual passengers would love to be able to use that extra 1.5 cubic meters of stateroom volume when they weren't sleeping.

I don't know whether we would have spent any more time in my last cruise ship stateroom if we had an extra 1.5 cubic meters of daytime space, since there was so much to do in the public areas of the ship, but it might have been nice. And if some closet technology had made it easier to manage clean clothes, dirty clothes, camera gear, astronomy gear (since it was an eclipse cruise), tourist purchases, etc., that would have been a big win.

But coming back to game terms, there's not much to say about the difference between a basic starship stateroom and a peak technology stateroom, except maybe that some passengers will pay a bit more, or you can get more passengers into the same amount of volume if the furniture in the common areas can reconfigure itself between use as a dining room, show hall, disco, casino, and gym just by flipping the control switches.

But most other stuff is the same across TL's. Super conductor wiring for transferring energy from a TL10 or TL15 power plant is probably going to be the same. The life support equipment is probably going to be the same. Basic sub-systems (like airlock machinery and decontamination equipment) would most likely be the same.

As above, manufacturing definitely advances, according to published rules that date back to the classic Trillion Credit Squadron rules. Maintenance may also advance (according to real world example), or degrade (because some things are easier to replace than repair when original manufacture is cheap), but maintenance is dependent on technological base (per the rules).

Applying all that to my example ship that's a TL12 and TL14 hybrid, and the advanced economic rules, I'd say that the entire ship would be built in a TL14 shipyard with, with components built with TL14 manufacturing, with designs that can be maintained with TL12 technology, except for the elements that require TL14. Some components would be manufactured with lower technology, because the exchange rate differences would outweigh the greater efficiency of more advanced manufacturing technology, but customers wouldn't see that because those are low-cost components anyway.

Specific numbers:
TL15 components must be imported, and cost two to six times list price, depending on rules I don't remember, plus the effects of speculative trade.
TL14 components cost list price in TL14 credits.
TL13 components cost half as much to make at TL14, but TL14 credit cost 1.5 times as much so the net cost is 0.75 times list price -- but there's not much advantage to including a lot of TL13 components.
TL12 components cost one-fourth as much to make at TL14, but TL14 credits cost 1.5×1.5 times as much, so the net cost is 0.5625 times list price.
TL11 components cost one-fourth as much to make at TL14, but TL14 credits cost 1.5^3 times as much, so the net cost is 0.84375 times list price; it might be cheaper to import them from a TL13 world.
TL10 components cost one-fourth as much to make at TL14, but TL14 credits cost 1.5^4 times as much, so the net cost is 1.265625 times list price, so it's probably cheaper to import them from a TL12 world.
Skipping to an extreme case, TL4 components -- say decorative fixtures in the common areas -- cost one-fourth as much to make at TL14, cut TL14 credits cost 1.5^10 times as much, so it definitely makes sense to import them from a TL4, TL5, or TL6 world rather than spending more than 109 times (!) list price on them.

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I'm not going to bother jumping (pun noted) into the discussion of drop tanks and jump capacitors; others seem to have that covered.